Topological 
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 resonating-valence-bond spin liquid on the square lattice

Chen, Jiyao; Poilblanc, Didier

doi:10.1103/physrevb.97.161107

Cited by 25 publications

(37 citation statements)

References 40 publications

(48 reference statements)

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“…However, investigation of classical dimer models at finite temperature [8] indicates that criticality and nonbipartiteness are compatible. In fact, our D = 3 PEPS, which realizes exactly an extended RVB state with (inter-sublattice) longerrange singlets, is known to possess an extended RK dimer liquid phase [63]. Also, it is likely that regions of (truly critical) RK phases exist also within our D = 5 and D = 7 PEPS manifolds.…”

Section: Discussionmentioning

confidence: 93%

Critical colored-RVB states in the frustrated quantum Heisenberg model on the square lattice

2019

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We consider a family of SU(2)-symmetric Projected Entangled Paired States (PEPS) on the square lattice, defining colored-Resonating Valence Bond (RVB) states, to describe the quantum disordered phase of the J 1 − J 2 frustrated Heisenberg model. For J 2 /J 1 ∼ 0.55 we show the emergence of critical (algebraic) dimerdimer correlations -typical of Rokhsar-Kivelson (RK) points of quantum dimer models on bipartite lattices -while, simultaneously, the spin-spin correlation length remains short. Our findings are consistent with a spin liquid or a weak Valence Bond Crystal in the neighborhood of an RK point.

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Section: Discussionmentioning

confidence: 93%

Critical colored-RVB states in the frustrated quantum Heisenberg model on the square lattice

2019

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“…Indeed, the norm of a PEPS can be naturally interpreted as a two-dimensional partition function and the question often poses itself in what phase the corresponding PEPS transfer matrix is. The paradigmatic example here is the resonating valencebond (RVB) wavefunction on the square lattice, for which the transfer matrix is known to be in a U(1) phase [43,44], and also other symmetric PEPS parametrization for (chiral) spin liquids seem to give rise to critical transfer matrices [45]. The relation between the critical properties of the transfer matrix, which are esssentially the properties of a two-dimensional classical system, the symmetries of the PEPS tensors, and the quantum properties of the PEPS wavefunction (physical correlation functions, entanglement spectra, etc.)…”

Section: Discussionmentioning

confidence: 99%

Approaching the Kosterlitz-Thouless transition for the classical XY model with tensor networks

et al. 2019

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We apply variational tensor-network methods for simulating the Kosterlitz-Thouless phase transition in the classical two-dimensional XY model. In particular, using uniform matrix product states (MPS) with non-abelian O(2) symmetry, we compute the universal drop in the spin stiffness at the critical point. In the critical low-temperature regime, we focus on the MPS entanglement spectrum to characterize the Luttinger-liquid phase. In the high-temperature phase, we confirm the exponential divergence of the correlation length and estimate the critical temperature with high precision.Our MPS approach can be used to study generic two-dimensional phase transitions with continuous symmetries.

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“…This superposition is highly entangled and breaks no symmetries [24,25]. The RVB state is, therefore, a candidate to describe the physics of quantum spin liquids [25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, the tensor network (TN) representation of RVB states has been put forward [40] and exact TN representation for RVB state on the square lattice [4,26,29] and topological Z 2 RVB states on the kagome lattice for both nearest-neighbor [24,40] and next-nearest-neighbor dimer coverings [25] have been introduced. Moreover, the TN construction of the RVB wave function has been applied to chiral spin liquids [28,41,42] as well as semionic [31] and fermionic [7] RVB states.…”

Section: Introductionmentioning

confidence: 99%

Topological Z2 resonating-valence-bond quantum spin liquid on the ruby lattice

Jahromi

Orús

2020

Phys. Rev. B

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We construct a short-range resonating valence-bond state (RVB) on the ruby lattice, using projected entangled-pair states (PEPS) with bond dimension D = 3. By introducing non-local moves to the dimer patterns on the torus, we distinguish four distinct sectors in the space of dimer coverings, which is a signature of the topological nature of the RVB wave function. Furthermore, by calculating the reduced density matrix of a bipartition of the RVB state on an infinite cylinder and exploring its entanglement entropy, we confirm the topological nature of the RVB wave function by obtaining non-zero topological contribution, γ = −ln 2, consistent with that of a Z2 topological quantum spin liquid. We also calculate the ground-state energy of the spin-1 2 antiferromagnetic Heisenberg model on the ruby lattice and compare it with the RVB energy. Finally, we construct a quantum-dimer model for the ruby lattice and discuss it as a possible parent Hamiltonian for the RVB wave function.

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Topological Z2 resonating-valence-bond spin liquid on the square lattice

Cited by 25 publications

References 40 publications

Critical colored-RVB states in the frustrated quantum Heisenberg model on the square lattice

Critical colored-RVB states in the frustrated quantum Heisenberg model on the square lattice

Approaching the Kosterlitz-Thouless transition for the classical XY model with tensor networks

Topological Z2 resonating-valence-bond quantum spin liquid on the ruby lattice

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